Short Selling and Margin Requirements for Exam FM

Short Selling Mechanics

Short selling involves borrowing shares from a broker and immediately selling them in the market, with the obligation to return the shares at a later date. The short seller profits if the price falls and loses if it rises. The basic profit on a short sale is S_0 - S_T - dividends paid - borrowing costs, where S_0 is the initial sale price and S_T is the repurchase (cover) price.

The short seller must deposit collateral (the initial margin) and pay any dividends declared during the short period to the share lender. The proceeds from the short sale are held by the broker, and both the proceeds and the margin deposit typically earn interest for the short seller. This interest income partially offsets the costs of maintaining the position.

From a cash flow perspective, at time 0 the short seller receives S_0 from the sale and deposits the margin. At time T, the short seller pays S_T to repurchase shares, returns them to the lender, and recovers the margin deposit plus accumulated interest. Any dividends paid during the holding period are owed to the share lender.

Margin Requirements

The initial margin is the deposit required when opening the short position, typically 50% of the short sale proceeds. For a stock sold short at $100, the initial margin deposit is $50, and the total account value is $150 (proceeds plus margin). The margin account value at any point is: proceeds from sale + initial margin + interest earned - current value of shares owed - dividends owed.

The equity in the margin account is the account value minus the current liability (the cost to cover the short position): Equity = S_0*(1 + initial margin ratio) + interest - S_current - dividends. The margin ratio is Equity / S_current. If this ratio falls below the maintenance margin (typically 25% to 30% of the current share value), the broker issues a margin call.

Example: Short 100 shares at $80, initial margin is 50% ($4,000 deposit). Total account = $12,000. If the stock rises to $90 and no dividends are paid, equity = 12,000 - 9,000 = $3,000. Margin ratio = 3,000/9,000 = 33.3%. If maintenance is 30%, no margin call occurs. But if the stock rises to $95, equity = 12,000 - 9,500 = $2,500, ratio = 2,500/9,500 = 26.3%, which is below 30%, triggering a margin call.

Computing the Margin Call Price

The margin call price can be found by solving for S_call where the margin ratio equals the maintenance requirement. If no dividends or interest are involved: (S_0 + margin - S_call) / S_call = maintenance margin ratio. Rearranging: S_call = (S_0 + margin) / (1 + maintenance ratio).

For example, if S_0 = $100, margin = $50 (50% of $100), and maintenance = 30%: S_call = (100 + 50) / (1 + 0.30) = 150 / 1.30 = $115.38. The stock price must rise above $115.38 to trigger a margin call.

When dividends or interest are included, modify the numerator: S_call = (S_0 + margin + interest earned - dividends paid) / (1 + maintenance ratio). On Exam FM, always check whether the problem specifies dividends or interest during the holding period.

Rate of Return on a Short Sale

The rate of return on a short sale is computed as the profit divided by the initial investment (the margin deposit). Profit = S_0 - S_T - dividends + interest on (S_0 + margin). Rate of return = profit / margin.

Example: Short at $100 with 50% margin ($50 deposit). The stock falls to $85 and pays a $2 dividend. Interest earned on the $150 account at 5% for one year is $7.50. Profit = 100 - 85 - 2 + 7.50 = $20.50. Rate of return = 20.50 / 50 = 41.0%. The leverage from margin amplifies returns in both directions.

If the stock had risen to $115 instead: Profit = 100 - 115 - 2 + 7.50 = -$9.50. Rate of return = -9.50/50 = -19.0%. Notice that the potential loss on a short sale is theoretically unlimited because there is no upper bound on how high the stock price can go.

Short Selling and Arbitrage Strategies

Exam FM tests short selling primarily in the context of arbitrage and derivatives. When the spot-forward parity relationship F = S_0 * e^(r-delta)*T is violated, an arbitrage strategy involves either buying the asset and shorting the forward (when the forward is overpriced) or short-selling the asset and going long the forward (when the forward is underpriced).

In a cash-and-carry arbitrage: buy the asset at S_0, borrow S_0 at rate r, and sell the forward at F. The profit at time T is F - S_0*e^(rT). In a reverse cash-and-carry: short sell the asset at S_0, invest S_0 at rate r, and buy the forward at F. The profit at time T is S_0*e^(rT) - F. The no-arbitrage forward price is where both profits are zero.

Understanding the exact cash flows from short selling, including the obligation to pay dividends and the interest earned on proceeds, is essential for constructing these strategies correctly on Exam FM.

Practical Considerations on Exam FM

Several practical details about short selling appear in exam problems. The short rebate is the interest rate paid on the short sale proceeds held by the broker. A lower rebate (or negative rebate) increases the cost of shorting. Some problems specify that the short seller receives a fraction of the interest on proceeds rather than the full amount.

Haircuts refer to additional margin requirements beyond the standard percentage. A haircut means the short seller must post more collateral, reducing leverage and returns. On Exam FM, these details are specified in the problem when relevant.

Study Tips and Common Pitfalls

The most common mistake is getting the profit direction wrong. Short sellers profit from price decreases: Profit = S_0 - S_T for a basic short (positive when S_T < S_0). Subtracting dividends (a cost to the short seller) and adding interest earned gives the complete picture.

Another frequent error is confusing the margin ratio calculation. For a short sale, equity = total account value minus shares owed. The maintenance margin ratio compares equity to the current value of shares owed (not the original sale price). Always set up the equation carefully and check the direction: rising prices reduce equity for short sellers.

Practice at least 4 margin call problems and 3 arbitrage problems involving short selling. Time yourself on these problems, as the calculations are straightforward but can be error-prone under pressure.